Semi-parametric bivariate correlated frailty models fit.

Description

Fit a semiparametric Bivariate correlated frailty model with Proportional Hazard structure. Here, frailty variances of pairs can be different.

Usage

bcfraildv(
  formula,
  data,
  initfrailp = NULL,
  frailty = c("gamma", "lognormal"),
  control = bcfraildv.control(),
  comonvar = FALSE,
  ...
)

Arguments

Value

An object of that contains the following components.

• coefficients - A vector of estimated Covariate coefficients.

• frailparest - A vector of estimated Frailty parameters i.e. frailty variance and correlation.

• stderr-A vector containing the Standard error of the Estimated parameters both covariate coefficients and frailty parameters.

• loglilk0- Log likelihood of without frailty model or loglik of coxph fit.

• loglilk-Log likelihood of Cox PH model with frailty.

• Iloglilk- Log likelihood of with frailty. For gamma fit it is I-likelihood or the likelihood after integrating out the frailty term.For lognormal fit it is the approximate likelihood.

• bhaz- an array containing unique event times and estimated baseline hazard.

• X-Matrix of observed covariates.

• time-the observed survival time.

• censor-censoring indicator.

• resid-the martingale residuals.

• lin.prid-the vector of linear predictors.

• frail-estimated Frailty values.

• iteration-Number of outer iterations.

• e.time-the vector of unique event times.

• n.event- the number of events at each of the unique event times.

• convergence-an indicator, 0 if converge and 1 otherwise.

Note

Parameters of Bivariate correlated gamma frailty model was estimated using a modified EM approach given in Kifle et al (2022) with modification for different frailty variances in a pair. Parameters of Bivariate correlated lognormal frailty model is based on the penalized partial likelihood approach by Rippatti and Palmgren (2000).

References

Kifle YG, Chen DG, Haileyesus MT (2022). Multivariate Frailty Models using Survey Weights with Applications to Twins Infant Mortality in Ethiopia. Statistics and Its Interface,106(4), 1\-10.

Rippatti, S. and Palmgren, J (2000). Estimation of multivariate frailty models using penalized partial likelihood. Biometrics, 56: 1016-1022.

See Also

bcfrailph, simbcfraildv

Examples

set.seed(4)
simdata<-simbcfraildv(psize=300, cenr= c(0.3),beta=c(2),frailty=c("gamma"),
frailpar=c(0.5,0.5,0.5),bhaz=c("weibull"),
bhazpar=list(shape =c(5), scale = c(0.1)),
covartype= c("B"),covarpar=list(fargs=c(1),sargs=c(0.5)))
dataa<-simdata$data

fitbcfrail=bcfraildv(Surv(time,censor)~ X1+frailty(PID) ,data=dataa,frailty="gamma")
fitbcfrail


# for lognormal

set.seed(18)
simdata<-simbcfraildv(psize=100, cenr= c(0.2),beta=c(1,-0.7,0.5),
frailty=c("lognormal"),frailpar=c(0.5,0.5,-0.25),bhaz=c("exponential"),
bhazpar=list(scale = c(0.1)),covartype= c("N","N","B"),
covarpar=list(fargs=c(0,0,1),sargs=c(1,1,0.5)),comncovar=2)
dataa<-simdata$data

#fit
fitbcfrlogn=bcfraildv(Surv(time,censor)~ X1+X2+X3+frailty(PID) ,data=dataa,frailty="lognormal")
fitbcfrlogn

set.seed(4)
simdata<-simbcfraildv(psize=300, cenr= c(0.3),beta=c(2),frailty=c("gamma"),
frailpar=c(0.5,0.5,0.5),bhaz=c("weibull"),
bhazpar=list(shape =c(5), scale = c(0.1)),
covartype= c("B"),covarpar=list(fargs=c(1),sargs=c(0.5)))
dataa<-simdata$data

## one can set the initial parameter for the frailty parameters
fitbcfrail=bcfraildv(Surv(time,censor)~ X1+frailty(PID) ,data=dataa,
frailty="gamma",initfrailp = c(0.2,0.2,0.4))
fitbcfrail

# Not run

#if covariates are not included
fitmoe=try(bcfraildv(Surv(time,censor)~0+frailty(PID),data=dataa,
frailty="lognormal"),silent = TRUE)

fitmoe=try(bcfraildv(Surv(time,censor)~1+frailty(PID),data=dataa),silent = TRUE)

# if control is not specified correctly.
# if one needs to change only max.iter to be 100,

fitmoe=try(bcfraildv(Surv(time,censor)~ X1+frailty(PID),data=dataa,
control=c(max.iter=100)),silent = TRUE)

#the correct way is
fitmoe=bcfraildv(Surv(time,censor)~ X1+frailty(PID),data=dataa,
control=bcfraildv.control(max.iter=100))
fitmoe

#if initial frailty parameters are in the boundary of parameter space
fitmoe=try(bcfraildv(Surv(time,censor)~ X1+frailty(PID),data=dataa,
initfrailp=c(0.2,0.3,1)),silent = TRUE)

fitmoe=try(bcfraildv(Surv(time,censor)~ X1+frailty(PID),data=dataa,
initfrailp=c(0,0.5,0.1)),silent = TRUE)

#if a frailty distribution other than gamma and lognormal are specified

fitmoe=try(bcfraildv(Surv(time,censor)~ X1,data=dataa,frailty="exp"),silent = TRUE)

# End Not run

Arguments for controlling bcfraildv fits.

Description

This is used to set various numeric parameters controlling a bcfraildv model fit as a single list.

Usage

bcfraildv.control(
  max.iter = 500,
  tol = 1e-04,
  eval.max = 500,
  iter.max = 500,
  trace = 0,
  abs.tol = 1e-20,
  rel.tol = 1e-10,
  x.tol = 1.5e-08,
  xf.tol = 2.2e-14,
  step.min = 1,
  step.max = 1
)

Arguments

Value

A list of control parameters.

See Also

bcfraildv

Parametric bivariate correlated frailty models fit.

Description

Fit a parametric Bivariate correlated gamma, inverse gaussian and power variance frailty models with Proportional Hazard structure.

Usage

bcfrailpar(
  formula,
  data,
  initfrailp = NULL,
  inithazp = NULL,
  initbeta = NULL,
  haz = c("weibull", "gompertz", "exponential"),
  frailty = c("gamma", "invgauss", "pv"),
  comonvar = TRUE,
  ...
)

Arguments

Value

An object of that contains the following components.

• coefficients - A vector of estimated Covariate coefficients.

• frailparest - A vector of estimated Frailty parameters i.e. frailty variance and correlation.

• basehazpar - A vector of estimated baseline hazard parameters i.e. scale and shape.

• stderr-A vector containing the Standard errors of the Estimated parameters with the order of frailty parameters,baseline hazard parameters and covariate coefficients.

• vcov- Variance Covariance matrix of the Estimated parameters.

• loglik-Log likelihood of the model.

• AIC-AIC of the model.

• BIC-BIC of the model.

• iterations-Number of outer iterations.SeeconstrOptim for further.

• convergence-An indicator of convergence. SeeconstrOptim for further.

Examples

set.seed(4)
simdata<-simbcfraildv(psize=500, cenr= c(0.3),beta=c(2),frailty=c("gamma"),
frailpar=c(0.5,0.5,0.5),bhaz=c("weibull"),
bhazpar=list(shape =c(5), scale = c(0.1)),
covartype= c("B"),covarpar=list(fargs=c(1),sargs=c(0.5)))
dataa<-simdata$data

fitbcfrail=bcfrailpar(Surv(time,censor)~ X1+frailty(PID) ,data=dataa,frailty="gamma")
fitbcfrail



set.seed(18)
simdata<-simbcfraildv(psize=300, cenr= c(0.3),beta=c(2),frailty=c("gamma"),
frailpar=c(0.5,0.5,0.4),bhaz=c("weibull"),
bhazpar=list(shape =c(5), scale = c(0.1)),
covartype= c("B"),covarpar=list(fargs=c(1),sargs=c(0.5)))
dataa<-simdata$data

#fit with power variance frailty distribution
fitbcfrail=bcfrailpar(Surv(time,censor)~ X1+frailty(PID) ,data=dataa,
frailty="pv")
fitbcfrail

## one can set the initial parameter for the frailty parameters
fitbcfrail=bcfrailpar(Surv(time,censor)~ X1+frailty(PID) ,data=dataa,initfrailp = c(0.4,0.3),
frailty="gamma")
fitbcfrail

# Not run

#if initial frailty parameters are in the boundary of parameter space
fitmoe=try(bcfrailpar(Surv(time,censor)~ X1+frailty(PID),data=dataa,
initfrailp=c(0.2,1)),silent = TRUE)

#if a frailty distribution other than gamma, invgauss or pv is specified

fitmoe=try(bcfrailpar(Surv(time,censor)~ X1,data=dataa,frailty="exp"),silent = TRUE)

# End Not run

Print bcfraildv

Description

Generics to print the S3 class bcfraildv.

Usage

## S3 method for class 'bcfraildv'
print(x, ...)

Arguments

Details

Calls print.bcfraildv().

Value

An object of print.bcfraildv, with some more human-readable results from bcfraildv object.

Note

The summary function is currently identical to the print function.

See Also

bcfraildv

Examples

set.seed(4)
simdata<-simbcfraildv(psize=300, cenr= c(0.3),beta=c(2),frailty=c("gamma"),
frailpar=c(0.5,0.5,0.5),bhaz=c("weibull"),
bhazpar=list(shape =c(5), scale = c(0.1)),
covartype= c("B"),covarpar=list(fargs=c(1),sargs=c(0.5)))
dataa<-simdata$data

fitbcfrail=bcfraildv(Surv(time,censor)~ X1+frailty(PID) ,data=dataa)
fitbcfrail
summary(fitbcfrail)

Print bcfrailpar

Description

Generics to print the S3 class bcfrailpar.

Usage

## S3 method for class 'bcfrailpar'
print(x, ...)

Arguments

Details

Calls print.bcfrailpar().

Value

An object of print.bcfrailpar, with some more human-readable results from bcfrailpar object.

Note

The summary function is currently identical to the print function.

See Also

bcfrailpar

Examples

set.seed(4)
simdata<-simbcfraildv(psize=500, cenr= c(0),beta=c(-1),frailty=c("gamma"),
frailpar=c(0.4,0.4,0.5),bhaz=c("weibull"),
bhazpar=list(shape =c(0.9), scale = c(2)),
covartype= c("B"),covarpar=list(fargs=c(1),sargs=c(0.5)))
dataa<-simdata$data ## the simulated data set

#fit
parbcfit=bcfrailpar(Surv(time, censor) ~ X1+frailty(PID),data=dataa)
parbcfit

Simulate data from bivariate correlated frailty models.

Description

Simulate data from bivariate correlated gamma or lognormal frailty models with one covariate.

Usage

simbcfraildv(
  psize,
  cenr = c(0),
  beta = c(0.5),
  frailty,
  frailpar = c(0.5, 0.5, 0.25),
  bhaz = c("weibull"),
  bhazpar = list(shape = c(0.5), scale = c(0.01)),
  covartype = c("B"),
  covarpar = list(fargs = c(1), sargs = c(0.5)),
  inpcovar = NULL,
  inpcen = NULL,
  comncovar = NULL
)

Arguments

Value

An object of class simbcfraildv that contain the following:

• data A data frame i.e, the simulated data set. IID is individual Id, PID is pair ID, time is the simulated survival time, censor is censoring indicator and X1 denote the simulated covariate.

• numberofpair The specified number of pairs.

• censoredrate The specified censored rate.

• fraildist The specified frailty distribution.

• frailpar The specified frailty parameters.

See Also

bcfraildv

Examples

set.seed(4)
simdata<-simbcfraildv(psize=300, cenr= c(0.3),beta=c(2),frailty=c("gamma"),
frailpar=c(0.5,0.5,0.5),bhaz=c("weibull"),
bhazpar=list(shape =c(5), scale = c(0.1)),
covartype= c("B"),covarpar=list(fargs=c(1),sargs=c(0.5)))
dataa<-simdata$data
head(dataa)


# If data generation is from bivariate correlated lognormal frailty model,
set.seed(18)
simdata<-simbcfraildv(psize=100, cenr= c(0.2),beta=c(1,-0.7,0.5),frailty=c("lognormal"),
frailpar=c(0.5,0.8,-0.25),bhaz=c("exponential"),
bhazpar=list(scale = c(0.1)),covartype= c("N","N","B"),
covarpar=list(fargs=c(0,0,1),sargs=c(1,1,0.5)))
dataa<-simdata$data
head(dataa)

# If common covariate is desired, i.e., here out of the three covariates 
#covariate 2 is common for the pair.
set.seed(18)
simdata<-simbcfraildv(psize=100, cenr= c(0.2),beta=c(1,-0.7,0.5),frailty=c("lognormal"),
frailpar=c(0.5,0.8,-0.25),bhaz=c("exponential"),
bhazpar=list(scale = c(0.1)),covartype= c("N","N","B"),
covarpar=list(fargs=c(0,0,1),sargs=c(1,1,0.5)),comncovar=2)
dataa<-simdata$data
head(dataa)

# If the data generation is from bivariate correlated gamma frailty model,
#weibull baseline and without covariate,
set.seed(4)
simdata<-simbcfraildv(psize=300, cenr= c(0.3),beta=NULL,frailty=c("gamma"),
frailpar=c(0.5,0.6,0.5),bhaz=c("weibull"),bhazpar=list(shape =c(5), scale = c(0.1)))
dataa<-simdata$data
head(dataa)

Print bcfraildv

Description

Generics to print the S3 class bcfraildv.

Usage

## S3 method for class 'bcfraildv'
summary(object, ...)

Arguments

Details

Calls print.bcfraildv().

Value

An object of print.bcfraildv, with some more human-readable results from bcfraildv object.

Note

The summary function is currently identical to the print function.

See Also

bcfraildv

Examples

set.seed(4)
simdata<-simbcfraildv(psize=300, cenr= c(0.3),beta=c(2),frailty=c("gamma"),
frailpar=c(0.5,0.5,0.5),bhaz=c("weibull"),
bhazpar=list(shape =c(5), scale = c(0.1)),
covartype= c("B"),covarpar=list(fargs=c(1),sargs=c(0.5)))
dataa<-simdata$data

fitbcfrail=bcfraildv(Surv(time,censor)~ X1+frailty(PID) ,data=dataa)
fitbcfrail
summary(fitbcfrail)

Print bcfrailpar

Description

Generics to print the S3 class bcfrailpar.

Usage

## S3 method for class 'bcfrailpar'
summary(object, ...)

Arguments

Details

Calls print.bcfrailpar().

Value

An object of summary.bcfrailpar, with some more human-readable results from bcfrailpar object.

Note

The summary function is currently identical to the print function.

See Also

bcfrailpar

Examples

set.seed(40)
simdata<-simbcfraildv(psize=500, cenr= c(0.3),beta=c(-1),frailty=c("gamma"),
frailpar=c(0.4,0.4,0.5),bhaz=c("gompertz"),
bhazpar=list(shape =c(0.09), scale = c(0.2)),
covartype= c("B"),covarpar=list(fargs=c(1),sargs=c(0.5)))
dataa<-simdata$data

fitbcfrail=bcfrailpar(Surv(time,censor)~ X1+frailty(PID) ,
data=dataa,haz="gompertz")
fitbcfrail
summary(fitbcfrail)